A family of rotation numbers for discrete random dynamics on the circle

We revisit the problem of well-defining rotation numbers for discrete random dynamical systems on the circle. We show that, contrasting with deterministic systems, the topological (i.e. based on Poincar\'{e} lifts) approach does depend on the choice of lifts (e.g. continuously for nonatomic randomness). Furthermore, the winding orbit rotation number does not agree with the topological rotation number. Existence and conversion formulae between these distinct numbers are presented. Finally, we prove a sampling in time theorem which recover the rotation number of continuous Stratonovich stochastic dynamical systems on $S^1$ out of its time discretisation of the flow.Comment: 15 page

Robustness of the O(NN) universality class

We calculate the critical exponents for Lorentz-violating O($N$) $\lambda\phi^{4}$ scalar field theories by using two independent methods. In the first situation we renormalize a massless theory by utilizing normalization conditions. An identical task is fulfilled in the second case in a massive version of the same theory, previously renormalized in the BPHZ method in four dimensions. We show that although the renormalization constants, the $\beta$ and anomalous dimensions acquire Lorentz-violating quantum corrections, the outcome for the critical exponents in both methods are identical and furthermore they are equal to their Lorentz-invariant counterparts. Finally we generalize the last two results for all loop levels and we provide symmetry arguments for justifying the latter

Rod-like Polyelectrolytes in Presence of Monovalent Salt

We investigate the properties of rigid polyelectrolyte solutions in presence of monovalent salt. The free energy within the Debye-H\"uckel-Bjerrum (DHBj) theory [M. E. Fisher and Y. Levin, {\it Phys. Rev. Lett.} 71, 3826 (1993)] is constructed. It is found that at thermodynamic equilibrium the polyelectrolyte solution consists of clusters composed of one polyion and various counterions. The distribution of the cluster densities is determined by finding the minimum of the Helmholtz free energy. The osmotic pressure and the average charge of the cluster are found and their dependence on Manning parameter $\xi$ is elucidated. A good agreement with the experimental results is obtained.Comment: 11 pages, Revtex (using twocolumn style), 15 figures and postscript file. Submitted to Macromomelecule

Amphiphile Adsorption on Rigid Polyelectrolytes

A theory is presented which quantitatively accounts for the cooperative adsorption of cationic surfactants to anionic polyelectrolytes. For high salt concentration we find that the critical adsorption concentration (CAC) is a bilinear function of the polyion monomer and salt concentrations, with the coefficients dependent only on the type of surfactant used. The results presented in the paper might be useful for designing more efficient gene delivery systems

Unfolding spinor wavefunctions and expectation values of general operators: Introducing the unfolding-density operator

We show that the spectral weights $W_{m\vec K}(\vec k)$ used for the unfolding of two-component spinor eigenstates $| {\psi_{m\vec K}^\mathrm{SC}} > = | \alpha > | {\psi_{m\vec{K}}^\mathrm{SC, \alpha}} > + | \beta > | {\psi_{m\vec{K}}^\mathrm{SC, \beta}} >$ can be decomposed as the sum of the partial spectral weights $W_{m\vec{K}}^{\mu}(\vec k)$ calculated for each component $\mu = \alpha, \beta$ independently, effortlessly turning a possibly complicated problem involving two coupled quantities into two independent problems of easy solution. Furthermore, we define the unfolding-density operator $\hat{\rho}_{\vec{K}}(\vec{k}_{i}; \, \varepsilon)$, which unfolds the primitive cell expectation values $\varphi^{pc}(\vec{k}; \varepsilon)$ of any arbitrary operator $\mathbf{\hat\varphi}$ according to $\varphi^{pc}(\vec{k}_{i}; \varepsilon) = \mathit{Tr}(\hat{\rho}_{\vec{K}}(\vec{k}_{i}; \, \varepsilon)\,\,\hat{\varphi})$. As a proof of concept, we apply the method to obtain the unfolded band structures, as well as the expectation values of the Pauli spin matrices, for prototypical physical systems described by two-component spinor eigenfunctions

Systematic evaluation of software product line architectures

The architecture of a software product line is one of its most important artifacts as it represents an abstraction of the products that can be generated. It is crucial to evaluate the quality attributes of a product line architecture in order to: increase the productivity of the product line process and the quality of the products; provide a means to understand the potential behavior of the products and, consequently, decrease their time to market; and, improve the handling of the product line variability. The evaluation of product line architecture can serve as a basis to analyze the managerial and economical values of a product line for software managers and architects. Most of the current research on the evaluation of product line architecture does not take into account metrics directly obtained from UML models and their variabilities; the metrics used instead are difficult to be applied in general and to be used for quantitative analysis. This paper presents a Systematic Evaluation Method for UML-based Software Product Line Architecture, the SystEM-PLA. SystEM-PLA differs from current research as it provides stakeholders with a means to: (i) estimate and analyze potential products; (ii) use predefined basic UML-based metrics to compose quality attribute metrics; (iii) perform feasibility and trade-off analysis of a product line architecture with respect to its quality attributes; and, (iv) make the evaluation of product line architecture more flexible. An example using the SEI’s Arcade Game Maker (AGM) product line is presented as a proof of concept, illustrating SystEM-PLA activities. Metrics for complexity and extensibility quality attributes are defined and used to perform a trade-off analysis